层流、紊流共存时雷利阶梯轴承静特性分析

以具有深浅腔的高速阶梯轴承为研究对象,在考虑油膜中同时存在层流、紊流两种流态以及轴承两端存在不同静压力的条件下,采用连续性方程推导了油膜深浅腔的压力分布,进而求出轴承上的压力分布、承载力和摩擦力等静态特性参数。研究结果表明,油腔最优结构参数随深腔紊流因子和轴承两端静压力的不同而变化。将特定条件下混合流态时油膜静态特性结果与单一层流流态时的结果进行了比较。     

A study of optimum load capacity of slider bearings lubricated with power law fluids

A general theoretical study of an infinitely wide lubricated slider bearing is presented, considering the lubricant to be an incompressible, isothermal, power law fluid. A set of algebraic equations is developed to obtain the pressure gradient for any value of the power law index. To illustrate the mathematical development, the set of equations is used to calculate the pressure gradient for two special forms of slider bearings, viz., inclined and parabolic slider bearings. In these two cases, the variation of pressure, load capacity, coefficient of friction, etc. for a range of fluid- and bearing-parameters is presented. In order to obtain optimum load capacity for an inclined and a parabolic slider bearing, the variations of load capacity, coefficient of friction, etc., with respect to the simultaneous changes of the inlet–oulet film height ratio and of the power law index of lubricants are also analysed. The results are presented both numerically and graphically. The results reveal that in the cases of an inclined and a parabolic slider bearings the inlet–outlet film height ratio for the optimum load capacity depends on the power law index of lubricants. Further, for each value of power law index, there exists a value of inlet–outlet film height ratio for which the frictional coefficient is minimum.     

Performance characteristics for the hydrostatic thrust bearing of a saw blade

A semi-analytical solution is presented to obtain the pressure distribution, the load capacity, the frictional moment and the lubricant flow rate for a laminar flow, hydrostatic bearing with its axis offset from thee axis of the saw blade. The general equations are developed and solved for a variable film thickness due to plate vibrations. It was found that the load, friction and lubricant flow rate are strong functions of film thickness variations , bearing number λ and the bearing offset from the rotation axis     

An analytical approach for analysis and optimisation of slider bearings with infinite width parallel textures

This paper introduces an analytical approach to study the textured surfaces in hydrodynamic lubrication regime. For this purpose, a method of integrating the Reynolds equation for slider bearings with surface discontinuities is presented. By introducing appropriate dimensionless parameters, analytical relations for various texture profiles in both indented and projected forms are delivered. These relations express the nature of mathematical dependence between textured bearing performance measures and geometrical/operational parameters. An optimisation procedure is employed to achieve the optimum texturing parameters promoting maximum load capacity, load capacity to lubricant flow rate ratio and minimum friction coefficient for asymmetric partially textured slider bearings.     

Effects of lubricant additives on the performance of hydrodynamically lubricated journal bearings

A non-Newtonian rheological model to investigate theoretically the effects of lubricant additives on the steady state performance of hydrodynamically lubricated finite journal bearings is introduced. In this model, the non-Newtonian behavior resulting from blending the lubricant with polymer additives is simulated by Stokes couple stress fluid model. The formed boundary layer at the bearing surface is described through the use of a hypothetical porous medium layer that adheres to the bearing surface. The Brinkman-extended Darcy equations are utilized to model the flow in the porous region. A stress jump boundary condition is applied at the porous media/fluid film interface. A modified form of the Reynolds equation is derived and solved numerically using a finite difference scheme. The effects of bearing geometry, and non-Newtonian behavior of the lubricant on the steady-state performance characteristics such as pressure distribution, load carrying capacity, side leakage flow, and coefficient of friction are presented and discussed. The results showed that lubricant additives significantly increase the load carrying capacity and reduce both the coefficient of friction and the side leakage as compared to the Newtonian lubricants.     

Optimal profiles for one dimensional slider bearings under technological constraints

The optimal slider bearing profile for maximum bearing load is studied by using direct constrained optimal control techniques. The constraints include the Reynolds and the energy equations. The energy equation takes into account the shear strain rate in the lubricant. The dependence of lubricant viscosity on temperature is considered. Technological constraints such as the maximum lubricant pressure and temperature and the minimum lubricant film thickness are included into the model. The realistic problem considered here yields optimal bearing profiles which are much more complex than the classical Rayleigh step bearing profile. The optimal bearing profile consists of an alternation of regions of constant height and more or less abrupt height variations. The number of constant height regions depends on the type of the constraint and in many cases is larger than three. The minimum value of the bearing height is one of the most important constraints. Four levels of model approximations have been tested. The most important model improvement is to take into account the temperature dependence of the lubricant viscosity. Several bearing design and operation parameters, such as bearing length, inlet height, sliding velocity and lubricant inlet pressure and temperature, have been considered. They all have complex influence on the optimal bearing profile.     

推力滑动轴承表面织构的优化设计

在推力滑动轴承表面设计轴对称分布的扇形直槽织构,以提高轴承的流体动压润滑性能。为对扇形直槽的参数(直槽的数目、深度和面积比)进行优化设计,将轴承的内外径、转速、润滑油黏度、轴承间隙以及直槽参数作为变量,求解不同变量值下的Reynolds方程,得到油膜承载力,运用最小二乘法对承载力的离散数据进行拟合,得到承载力的拟合函数,并推导出摩擦因数的表达式。针对"轴承间隙已知,要求承载力最大或者摩擦因数最小,以及承载力已知,要求轴承间隙最大或者摩擦因数最小"这四种约束条件及优化目标,利用承载力和摩擦因数的拟合公式,得到对应的直槽参数的最优值。通过数值试验,将拟合公式计算的承载力、轴承间隙和摩擦因数与直接求解Reynolds方程得到的结果进行对比,验证了直槽参数优化结果的正确性。设计加工三种具有不同直槽数目和深度的扇形直槽织构并进行摩擦试验,通过对比摩擦因数的计算值和试验值后发现,承载力和摩擦因数的拟合公式在趋势上是正确的,直槽参数的优化结果是可信的。     

The Effects fo Speed,Load, and Film Thickness on the Performance of Gas-Lubricated,Tilting-Pad Journal Bearings

This paper deals with the effects of lubricant compressibility on the pressure profile and total load capacity in a partial journal bearing; pivot pressure as a measure of shoe load capacity; shoe friction characteristics; and optimum shoe clearnace ratios for various speeds. The parameter A is used as an indicator of the compressibility effect of gas in the bearing clearance.     

Lubricant additives effects on the hydrodynamic lubrication of misaligned conical–cylindrical bearings

Conical–cylindrical bearings are used in electrohydraulic servo systems to improve the control accuracy, eliminate the static friction and increase the normal load‐carrying capacity. A non‐Newtonian rheological model to investigate theoretically the effects of lubricant additives on the performance of misaligned conical–cylindrical bearings is proposed in this study. In this model, the non‐Newtonian behaviour resulting from blending the lubricant with polymer additives is simulated by Stokes couple stress fluid model. The formed boundary layer at the bearing surface is described through the use of a hypothetical porous medium layer that adheres to the bearing surface. The Brinkman‐extended Darcy equations are utilised to model the flow in the porous region. A stress jump boundary condition is applied at the porous media/fluid film interface. The misalignment of the cylinder rod is also considered. A modified form of the Reynolds equation is derived and solved numerically using a finite difference scheme. The effects of bearing geometry and non‐Newtonian behaviour of the lubricant on the steady‐state performance characteristics such as pressure distribution, load‐carrying capacity and coefficient of friction are presented and discussed. The results showed that lubricant additives significantly increase the load‐carrying capacity and reduce the coefficient of friction as compared to the Newtonian lubricants. Furthermore, the misalignment of the piston rod has significant effects on the performance of conical–cylindrical bearings. Copyright © 2007 John Wiley & Sons, Ltd.     

Thermohydrodynamic analysis of journal bearings lubricated with couple stress fluids

Thermohydrodynamic analysis of journal bearings is extended to include couple stress effects in lubricants blended with high polymer additives. Based on the micro-continuum theory, a modified energy equation is derived and then is simultaneously solved with the heat transfer equation as well as the modified Reynolds equation. The effects of couple stress on the key performance of a finite journal bearing, such as maximum temperature, shaft temperature, load capacity, friction force, friction coefficient, and side leakage flow, are presented. The results have shown that lubricants with couple stresses, compared with Newtonian lubricants, not only yield an obvious increase in load capacity and decrease in friction coefficient, but also produce a lower bearing temperature field. Thus it can be concluded that the lubricant with couple stress does improve the performance of journal bearings.     

多叶动压气体滑动轴承静态特性的有限差分算法

多叶动压气体滑动轴承因其结构简单、摩擦阻力低、旋转精度高和无环境污染等优点,在高速离心分离机、空气压缩机和透平膨胀机等旋转机械中应用广泛。为探究多叶动压气体滑动轴承的静态性能,通过数学变换将三叶动压轴承的气体润滑Reynolds方程转化为标准偏微分方程形式,利用有限差分法和超松弛迭代法进行数值求解,研究气膜厚度和气膜压力分布、承载力、摩擦因数和质量流量等静态性能,随偏心率、预负荷系数、轴承数、长径比及瓦块分布位置的变化规律。结果表明：三叶轴承的承载力和轴颈表面摩擦因数随偏心率和长径比的增加而增加,而偏位角和质量流量随偏心率和预负荷系数的增加则呈现出相反的变化趋势;随着轴承数和预负荷系数的增大,承载力和摩擦因数显著提高,偏位角和质量流量则逐渐减小;瓦块分布位置对三叶动压气体滑动轴承的静态性能影响显著,其中瓦上承载方式的承载力、偏位角和质量流量明显高于瓦间承载方式。     

Performance analysis of a fully textured hybrid circular thrust pad bearing system operating with non-Newtonian lubricant

The present paper deals with the theoretical investigation of the influence of dimple geometry on fully textured hybrid thrust pad bearing and operating with non-Newtonian lubricant. The modified Reynolds equation which governs the flow of non-Newtonian lubricant in the clearance space has been solved using Finite Element Method. The simulated results indicate that the values of load carrying capacity, frictional power loss, maximum pressure and fluid film stiffness coefficient are significantly affected by the behavior of lubricant. The results presented in the study are expected to aid in determining the optimum value of dimple diameter and depth for the optimum bearing performance.     

Step slider bearing with viscoelastic lubricant

The performance of an idealized step slider bearing with a viscoelastic lubricant is investigated theoretically. The elasticity of the lubricant is characterized by a dimensionless number α. The effects of the elasticity of the lubricant on the pressure, load-bearing capacity, frictional resistance, coefficient of friction and maximum film thickness were studied in detail and are presented in several graphs and tables.     

Porous inclined stepped composite bearings with micropolar fluid

Abstract

This paper describes the theoretical analysis of the effect of micropolar fluid on the lubrication characteristics of porous inclined stepped composite bearing. The lubricant with additives in the film region and also in the porous region is modelled as Eringen's micropolar fluid, which is characterised by the presence of suspended rigid particles with microstructures. The generalised Reynolds type equation is derived for the most general porous bearing configuration (porous composite bearings) lubricated with micropolar fluid. The closed form expressions are obtained for the fluid film pressure, load carrying capacity, frictional force and coefficient of friction. These expressions can be utilised to obtain the performance characteristics of four different bearing systems, namely, porous plane inclined slider, porous composite tapered land bearing, porous stepped bearing and composite porous tapered concave bearing. It is observed that the micropolar fluid lubricants provide an increased load carrying capacity and decreased coefficient of friction as compared to the corresponding Newtonian case.     

Surface roughness effects on thermo‐hydrodynamic lubrication of journal bearings lubricated with bubbly oil

In this paper, the combined effect of surface roughness and bubbles content on the hydrodynamic performance of journal bearings is studied. In the analysis, it is assumed that the bearing and shaft surfaces are covered with homogeneous isotropic roughness, the air bubbles are evenly distributed through the lubricant and the bubble size is very small. The modified Reynolds equation governing the pressure generation in the bearing gap for compressible fluid is solved simultaneously with the energy equation. Temperature and pressure distributions, coefficient of friction, bearing load capacity and attitude angle as affected by surface roughness, bubble content and some bearing parameters are presented. Results showed that the bearing load carrying capacity is higher at higher values of average roughness and higher bubble content as a direct consequence of the higher pressure values attained, and the average roughness and the bubbles content had no significant effect on the attitude angle. Copyright © 2006 John Wiley & Sons, Ltd.     

热效应对粗糙表面倾斜轴颈轴承润滑性能的影响

联立基于平均流量模型的广义Reynolds方程、三维能量方程和固体热传导方程等,计算了计及热效应时,不同表面形貌和轴颈倾斜角下的轴承油膜压力、油膜温度、油膜反力、端泄流量、摩擦系数和保持轴承稳定工作的力矩.考虑和不考虑热效应的轴承润滑特性计算结果表明,计入热效应时,表面形貌和润滑油粘压效应对偏心率较大的轴颈倾斜轴承润滑性能影响较大.     

Lubrication of a narrow porous journal bearing with a couple stress fluid

This paper describes a theoretical investigation of the rheological effects of couple stress fluids on the performance of narrow porous journal bearings. A most general modified Reynolds equation is derived for narrow porous journal bearings using the Stokes constitutive equations for couple stress fluids. The fluid in the film region and in the porous region has been modelled as a couple stress fluid. The analysis takes into account velocity slip at the porous interface using the Beavers‐Joseph criterion. A closed‐form expression for field pressure is obtained for narrow journal bearings. Eigen‐type expressions for field variations are obtained. The dimensionless load‐carrying capacity, attitude angle, and coefficient of friction are presented for different operating parameters. It is observed that narrow porous journal bearings with couple stress fluids as lubricant show a significant increase in load‐carrying capacity with reduced coefficient of friction as compared to the Newtonian case. The present study predicts the effects of the percolation of polar additives (microstructures) into the porous matrix on the bearing performance.     

Effect of air bubbles on externally pressurized bearing performance

A numerical study is made for externally pressurized bearings lubricated with incompressible fluid and finely dispersed air bubbles, taking into consideration the variation in lubricant physical properties due to pressure and temperature variations along the flow. The air bubbles are seen to improve the pressure distribution, to avoid cavitation that occurs because of the centripetal force, to improve the bearing load-carrying capacity and to decrease both the lubricant mass flow rate and the frictional power consumed in rotor rotation.     

Thermohydrodynamic Analysis and Thermal Management of Spherical Spiral Groove Gas Bearings

A thermohydrodynamic model of spherical spiral groove bearings is presented by considering the effect of bearing temperature change on the material property of lubricant, gas flow characteristics in the grooves, and thermal energy transported in the entire bearing system. A gas mixing model in the grooves is introduced as the boundary condition to solve the bearing temperature distribution simultaneously with the heat conduction at the shaft and the housing. The bearing and rotor expansion caused by temperature increases, which is considerable compared to bearing clearance, is also examined. Prediction results show that the thermal expansion determined by actual bearing clearance has a crucial influence on the bearing load capacity. Manufacturing bearings with proper materials has significant effects on controlling thermal expansion effects on the bearing performance. The load capacity, which corresponds to the lubricant gas pressure, and gas suck flow rate have the same variation tendencies as the variation in groove depth and spiral angle. These similar tendencies have an opposite influence on the temperature and result in the temperature increase not being affected by the variation in grooves. However, varying the groove characteristics has a similar effect in carrying away the thermal energy as the variation in heat transfer coefficient, which could significantly control the temperature increase at the same time.     

Tilting effects on the performance of hydrostatic and hybrid gas thrust bearings

A hydrostatic gas thrust bearing is analysed to determine the effect of tilting on its performance characteristics. The governing Reynolds Equation is solved simultaneously with the mass flow rate equation by numerical methods to determine the inlet pressure and the pressure distribution throughout the pad. It is shown that the load, friction, and lubricant mass flow rate are strong functions of the bearing number λ, restrictor coefficient λ_o, supply pressure and tilt parameter